04/09/2015

Introduction

Cybernetics

  • Gunnery Control and Norbert Wiener

  • "The world, understood cybernetically, was a world of goal-oriented feedback mechanisms with learning. Cybernetics,then, took computer-controlled gun control and layered it in an ontologically indiscriminate fashion across the academic disciplinary board."

  • Gunnery Control and Jay Forrester

What I tried to do

  • Less than fully rational agents are hard

  • Start from the opposite direction

  • Use simple trial and error

Feedback-Feedfoward Taxonomy

  • Feedback vs Feedforward

  • Ramsey Cass Koopmans - RBC - Learning
  • IS-LM models
  • Here

Alternatives

  • Zero-Intelligence (Plus)

  • Probe and Adjust

  • Gjerstad and Dickhaut

Zero Knowledge Microeconomics

The Agent problem

Enters the PI Controller

Zero-Knowledge Seller Demo

Formally

  • A seller wants to sell \(y^*\) units of a good each day. Today he charged price \(p_t\) and sold \(y_t\) units. How should he sets tomorrow's price \(p_{t+1}\)

  • \(e_t = y^* -y_t\)

  • \(p_{t+1} = a e_t + b \sum_0^t e_{\tau} d\tau + c \frac{de_t}{d_t}\)

Advantages

  • Trial and Error

  • Modular

  • Can be extended to buying

Adapting over Learning - Change in Demand

Adapting over Learning - Change in Endowment

From Zero Knowledge Traders to Zero Knowledge Firms

Zero Knowledge Firms

  • Multiple independent control problems

  • Need to set production rates that maximize profits

  • Lower frequency

Multiple Controls and Fixed Target

Two Optimization Strategies

  • How to choose production?

  • Hill-Climbing

  • Marginal Maximizer

Why I Liked Hill-Climbing

Why I Abandoned Hill-Climbing-1

Why I Abandoned Hill-Climbing-2

Marginal Maximizer

  • Profits are maximized when marginal benefits equal marginal costs

  • \(p_t + \mu_p = w_t + \mu_w\)

  • Use a PID with error \(p_t + \mu_p - w_t + \mu_w\)

Simple Marginal Example

Independent Control and Flexible Target

Monopolist, known price impacts

Competitive, known price impacts

Learning price impacts

  • PI trial and error produce paired data \(p_t,y_t\)

  • Can run a linear regression over them to discover \(\mu_p\)

  • Use Kalman Filters

Learning works

Zero Knowledge Supply Chains

Sticky Prices

  • Sticky prices and price rigidities

  • Why are prices sticky?

  • A model where sticky prices are superior to flexible ones

If you ever get lost

Undelayed

10 Days Delay

20 Days Delay

Stickiness Deals with Delays

Supply-Chains as a Source of Delays

  • PID seller changes price to elicit a response in the quantity demanded

  • Maximization happens at a lower frequency than price changes

  • Downstream zero knowledge firms adapt labor slowly to upstream price changes

Delays break supply-chains

## NULL

Stickiness restores equilibrium

## NULL

Sticky supply chains get to equilibrium's price

Sticky supply chains get to equilibrium's quantity

Learning degrades with sticky delays and supply-chains

Zero Knowledge Macroeconomics

Sticky Prices in Retrospect

  • Price rigidities as relative speed
  • Leijonhufvud "Keynes and the Keynesians"

Compare the two firms

  • Marshallian firm
  • Fixes short term differences in netflow by changing prices
  • Maximizes profitability over time by changing production
  • Keynesian firm
  • Fixes short term differences in netflow by changing production
  • Maximizes profitability over time by changing prices
  • For this section, assume infinitely elastic labor supply

Marshallian Micro

Keynesian Micro

Macroeconomics

  • I mostly stay clear from macro ABM
  • Demand equals wages paid
  • No savings

Marshallian Macro

Keynesian Macro

Demand Shock

Keynesian is faster

Keynesian is worse

Too fast, too furious

Labor flexibility as speed

Labor flexibility as productivity

Conclusion

Conclusion

  • Where to go from here
  • What has been cut out
  • Thank you!